The Bellman Function for a Parametric Family of Extremal Problems in BMO

Let I be an interval of the real line and 〈⋅〉 I be the corresponding integral average. We describe the behavior of the Bellman function for the functional F ( φ ) = 〈 f  ∘  φ 〉 I , φ ∈ BMO( I ), as f ranges over some parametric family of functions. Thereby, we once again demonstrate the power of the...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 243; no. 6; pp. 907 - 916
Main Author Osipov, N. N.
Format Journal Article
LanguageEnglish
Published New York Springer US 23.03.2020
Springer
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
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Summary:Let I be an interval of the real line and 〈⋅〉 I be the corresponding integral average. We describe the behavior of the Bellman function for the functional F ( φ ) = 〈 f  ∘  φ 〉 I , φ ∈ BMO( I ), as f ranges over some parametric family of functions. Thereby, we once again demonstrate the power of the methods developed recently by V. I. Vasyunin, P. B. Zatitskiy, P. Ivanishvili, D. M. Stolyarov, and the author.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04591-5